confidence interval

Part I.
Suppose the coach of the football team wants to estimate the proportion of the population of fans who support his current starter lineup. The coach wants the estimate to be .04 of the true proportion. Assume a 99 percent level of confidence. The coach estimated the proportion supporting the current starter lineup to be .60.

Answer the following questions:

1. Construct a 99% confidence interval using a sample size of 50, then of 100, then of 1,000.
2. How did changing the sample size affect the size of the interval?
3. What is the error of the estimate for each of these sample sizes?
4. How large of a sample is required for the error of the estimate to be within +.04 of the population proportion?
5. How large would the sample have to be if the coach of the team did not give an estimated proportion?

Show your work.

Part II.
A study is being done to determine how many hours college students study before taking an exam. A pilot study indicated that the mean time during the week of the exam is 4 hours, with a standard deviation of 1 hour. It is desired to estimate the mean study time within ½ hour. The 80 percent degree of confidence is to be used.